Deductions & credits

This is a *very* complicated area. You can figure it out but it requires effort.

See these resources:

https://turbotax.intuit.ca/tips/how-are-taxes-assessed-for-u-s-citizens-working-in-canada-347

https://www.thetaxadviser.com/newsletters/2018/feb/tax-treaty-benefits-us-citizens-residents.html

https://www.irs.gov/businesses/international-businesses/canada-tax-treaty-documents

A couple of key concepts/things to understand. Please realized this is a volunteer forum and while I have some experience in this, I do not have any direct US/Canadian experience and the details matter.

• you say you will be going back and forth. figure out how much presence or what type of presence is need to may you a Canadian tax-resident. https://www.canada.ca/en/revenue-agency/services/tax/international-non-residents/information-been-mo...
  • if Canada taxes you as a resident it may tax you on all of your income by default . the tax treaty may be very important in that case. If not and you are just taxed on your Canadian job income, everything will be much easier.
• generally if you earn wages in another country
  • the other country will tax based the location of the work
  • the US will tax based on citizenship (or perm residence status)
  • if you are in the other country for something like 330 days out any 12 months including any day in the tax year (I think) you can claim the foreign earned-income exclusion. That will remove the income from your US taxes (but your marginal rate will not decrease, it is still figured with your phantom income). This is complicated and detailed with various limits and requirements. See https://www.irs.gov/individuals/international-taxpayers/foreign-earned-income-exclusion and https://www.irs.gov/forms-pubs/about-form-2555
• If you don't qualify for that (or even if you do) there is also the US Foreign Tax Credit. For foreign source income like wages earned in another country you get a credit (much better than a deduction) for taxes (income only not social security or other) paid to a foreign country. Again various limits and conditions apply.  Generally foreign taxes are much higher than US taxes so this will usually wipe out any US tax owned on the foreign income. See https://www.irs.gov/individuals/international-taxpayers/foreign-tax-credit
• be careful of your green card status. e.g. be careful not to appear to be abandoning your US permanent residence. If you are going back and forth frequently I don't think that will be a problem. But if you have a place of abode there for long stretches of time just be careful. https://citizenpath.com/lose-permanent-resident-status/
• re: social security there is a "Totalization" Agreement (treaty) with Canada. check if and/or other research for details. It appears that you pay social taxes in whichever country you are physically working, but that you can somehow claim credit in either country for taxes paid to the other country. the devil may be in the details. 
  • https://www.ssa.gov/international/Agreement_Pamphlets/canada.html
  • https://www.ssa.gov/international/Agreement_Texts/canada.html
  • https://cardinalpointwealth.com/2019/04/10/understanding-the-canada-u-s-totalization-agreement/